I have found that you can actually run and it does not break your combo. Soft pika warm pika charging up anew happy pika shirt  if you look in the Pokédex, the animations you can play will correspond to when a Pokemon is going to flee. So with growlithe (one I am hunting) it has 2 animations. The first is the normal one, the second is the one it does just before it flees. When that animation plays you can run away and it won’t break the combo. Saved my combo resetting so many times! My first shiny chain I was trying for a shiny caterpie in Viridian Forest. Got to about 65, and suddenly shiny bulbasaur appeared. I couldn’t resist. As soon I caught it, shiny pikachu appeared, so I grabbed that too. Then shiny metapod appeared.